Many American schoolchildren are failing or seriously underachieving in mathematics. Compared to students in other western nations, U.S. students rank low in math. Math illiteracy limits an individual's educational and vocational opportunities and quality of life. Yet research on mathematics disabilities has progressed more slowly than has research on reading disabilities. Through a four-year longitudinal study of 400 children, starting in kindergarten and ending in third grade, the proposed project will forge new, theoretically based directions for the study of mathematics disabilities. In particular, the project will (1) employ the cutting edge methodology of growth mixture modeling to define a priori classes of growth in math precursor skills in kindergarten and use these classes to predict rate of achievement in conventional math in first through third grades (2) examine growth in math precursors in relation to early reading, language, and intellectual abilities; (3) uncover the underpinnings of specific skill deficiencies in math, such as deficits in number-fact retrieval; (4) investigate whether risk status in young children can be moderated by teaching and family factors; and (5) relate children's scores on a state-mandated, standards-based math test in third grade to their early achievement growth patterns. The accomplishment of these aims will lead to a conceptual model of achievement growth in primary school children with, or who are at risk for, mathematics disabilities, that considers cognitive, teacher, and home factors as well as demographic information (e.g., race, socioeconomic status, and gender). The proposed work has practical as well as theoretical significance. States are now using high stakes tests to make important educational decisions. Typically, state-mandated math testing begins at the end of third grade, and there are serious consequences for children who fail the tests. Little is known about the early achievement growth trajectories of children who fail to meet state standards. Early identification of children at risk can prevent later mathematics disabilities. We will use our findings to develop a scientifically grounded yet teacher accessible tool to identify children at risk for long-term mathematics disabilities. We also expect the findings to have direct applications for the development of evidence-based math interventions. [unreadable] [unreadable]